The easist explanation is that the components of the amplifier have capacitance, and that capacitance takes time to charge and discharge. Essentially, the amplifier is not able to swing its output fast enough to keep up with a high-frequency input.

The in-depth explanation is that if you do an impedance analysis of the amplifier, and get the frequency response plot of the amplifier, you have the answer to your question. In amplifiers, there is always the capacitance effect, and capacitance impedance drops as the frequency of the input signal increases. (NB: Z=1/jwC where w=angular frequency of the signal) So the gain of the amplifier in the frequnecy response plot will fall to zero as w increases. The physical explanation of why the capacitance drops as frequency increases has been explained by chroot.